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We study the first non-planar correction to gluon scattering amplitudes in${\cal N}=4$ SYM theory. The correction takes the form of a double tracepartial amplitude and is suppressed by one power of $1/N$ with respect to theleading single trace contribution. We extend the duality between planarscattering amplitudes and null polygonal Wilson loops to the double traceamplitude. The new duality relates the amplitude to the correlation function oftwo infinite null polygonal Wilson lines that are subject to a quantumperiodicity constraint. We test the duality perturbatively at one-loop orderand demonstrate it for the dual string in AdS. The duality allows us to extendthe notion of the loop integrand beyond the planar limit and to determine itusing recursion relations. It also allows one to apply the integrability-basedpentagon operator product expansion approach to the first non-planar order.

Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction